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On the Gardner Problem for Phase-Locked Loops

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Abstract

This paper shows the possibilities of solving the Gardner problem of determining the lock-in range for multidimensional phase-locked loop models. Analytical estimates of the lock-in range for a third-order system are obtained for the first time by developing analogues of classical stability criteria for the cylindrical phase space.

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Notes

  1. In the literature on PLL, the use of a zero pole is recommended for extending the pull-in range, while additional stable links are recommended for improving the filtering properties [8].

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Funding

This work was supported by the Russian Science Foundation, project no. 19-41-02002.

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Authors and Affiliations

  1. St. Petersburg State University, 198504, St. Petersburg, Russia

    N. V. Kuznetsov, M. Y. Lobachev, M. V. Yuldashev & R. V. Yuldashev

  2. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, 199178, St. Petersburg, Russia

    N. V. Kuznetsov

  3. University of Jyväskylä, Jyväskylä, Finland

    N. V. Kuznetsov

Authors
  1. N. V. Kuznetsov
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  2. M. Y. Lobachev
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  3. M. V. Yuldashev
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  4. R. V. Yuldashev
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Corresponding author

Correspondence to N. V. Kuznetsov.

Additional information

Translated by I. Ruzanova

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Kuznetsov, N.V., Lobachev, M.Y., Yuldashev, M.V. et al. On the Gardner Problem for Phase-Locked Loops. Dokl. Math. 100, 568–570 (2019). https://doi.org/10.1134/S1064562419060218

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  • DOI: https://doi.org/10.1134/S1064562419060218

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